Problem: Simplify; express your answer in exponential form. Assume $k\neq 0, q\neq 0$. $\dfrac{{k^{4}}}{{(k^{-3}q^{-5})^{2}}}$
Solution: To start, try working on the numerator and the denominator independently. In the numerator, we have ${k^{4}}$ to the exponent ${1}$ . Now ${4 \times 1 = 4}$ , so ${k^{4} = k^{4}}$ In the denominator, we can use the distributive property of exponents. ${(k^{-3}q^{-5})^{2} = (k^{-3})^{2}(q^{-5})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{k^{4}}}{{(k^{-3}q^{-5})^{2}}} = \dfrac{{k^{4}}}{{k^{-6}q^{-10}}}$ Break up the equation by variable and simplify. $\dfrac{{k^{4}}}{{k^{-6}q^{-10}}} = \dfrac{{k^{4}}}{{k^{-6}}} \cdot \dfrac{{1}}{{q^{-10}}} = k^{{4} - {(-6)}} \cdot q^{- {(-10)}} = k^{10}q^{10}$.